Simplify the following expression: $n = \dfrac{r^2 - r - 12}{r + 3} $
First factor the polynomial in the numerator. $ r^2 - r - 12 = (r + 3)(r - 4) $ So we can rewrite the expression as: $n = \dfrac{(r + 3)(r - 4)}{r + 3} $ We can divide the numerator and denominator by $(r + 3)$ on condition that $r \neq -3$ Therefore $n = r - 4; r \neq -3$